Singular learning theory and statistical inference

Group Leader: Vadim Munteanu

Study Team: Vadim Munteanu

Supervisor: Calin Lazaroiu

Scheme:

A. Basic theory of Bayesian learning

B. Measures of model fitness; the KL divergence.

C. The Watanabe free energy and its relation to the KL landscape

D. Asymptotic expansion of Watanabe's free energy (the Watanabe formula)

E. Connection to Polchinski RG flow and the optimal transport problem

F. Sampling through random processes

G. Numerical studies

Bonus: History of Bayesian inference and of Bayesian models of learning.

References:

S. Watanabe, Mathematical theory of Bayesian statistics

S. Watanabe, Algebraic geometry and statistical learning theory

S. Watanabe, Recent advances in algebraic geometry and Bayesian statistics

J.W. Lamperti, Probability: a survey of the mathematical theory

Karatzas & Schreve, Brownian motion and stochastic calculus

Bernardo & Smith, Bayesian theory

More references here and here.